Decentralized Optimization Over Tree Graphs

This paper presents a decentralized algorithm for non-convex optimization over tree-structured networks. We assume that each node of this network can solve small-scale optimization problems and communicate approximate value functions with its neighbors based on a novel multi-sweep communication prot...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 189; no. 2; pp. 384 - 407
Main Authors: Jiang, Yuning, Kouzoupis, Dimitris, Yin, Haoyu, Diehl, Moritz, Houska, Boris
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2021
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Computational geometry
Convex analysis
Convexity
Engineering
Mathematics
Mathematics and Statistics
Nodes
Operations Research/Decision Theory
Optimization
Parallel processing
Theory of Computation
Topology
Tree graph
Decentralized optimization
Dynamic programming
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This paper presents a decentralized algorithm for non-convex optimization over tree-structured networks. We assume that each node of this network can solve small-scale optimization problems and communicate approximate value functions with its neighbors based on a novel multi-sweep communication protocol. In contrast to existing parallelizable optimization algorithms for non-convex optimization, the nodes of the network are neither synchronized nor assign any central entity. None of the nodes needs to know the whole topology of the network, but all nodes know that the network is tree-structured. We discuss conditions under which locally quadratic convergence rates can be achieved. The method is illustrated by running the decentralized asynchronous multi-sweep protocol on a radial AC power network case study.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01828-9